Electrical Engineering

Renewable Energy & Efficiency

SEER to EER Conversion (Air Conditioner Efficiency)

EER = SEER × 0.875 (approximate) · EER = -0.02 × SEER² + 1.12 × SEER - 0.5 (more precise)

Electrical Installations

Lux & Lumens Calculator

Lumens = Lux × Area (m²) · Lux = f( Activity )

Energy & Billing

Appliance Load Calculator

Pₜ = Σ(Pᵢ × Qᵢ)

Renewable Energy & Efficiency

Specific Energy Consumption

SEC = Energy Consumed(kWh) / Output (units)

Renewable Energy & Efficiency

Lighting Lumen Efficacy

η = Luminous Flux(lm) / Power(W)

Renewable Energy & Efficiency

Coefficient of Performance (COP)

COP = Useful Heat/Cooling Output / Work Input

Renewable Energy & Efficiency

Energy Efficiency Ratio (EER)

EER = Cooling Output (BTU/hr) / Power Input (W)

Renewable Energy & Efficiency

Battery Backup Time

t = Ah / I_load

Renewable Energy & Efficiency

Battery Energy (Watt-Hours)

Wh = V × Ah

Renewable Energy & Efficiency

Battery Capacity (Amp-Hours)

Ah = I × t

Renewable Energy & Efficiency

Number of Solar Panels Needed

N = Total Load Energy / (Panel Output × Sun Hours)

Renewable Energy & Efficiency

Solar Panel Power Output

P = Irradiance × Area × Efficiency

Electric Machines

Motor Full-Load Current (Three Phase)

I = P / (√3 × V × cos θ × η)

Electric Machines

Motor Full-Load Current (Single Phase)

I = P / (V × cos θ × η)

Electric Machines

Watts to Horsepower Conversion

HP = P(W) / 746

Electric Machines

Horsepower to Watts Conversion

P(W) = HP × 746

Electrical Installations

Cable Ampacity Derating Factor

I_derated = I_rated × k₁ × k₂

Electrical Installations

Earthing Resistance (Rod Electrode)

R = ρ / (2π·L)

Electrical Installations

Power Loss Percentage

%Loss = (P_loss / P_input) × 100

Electrical Installations

Circuit Breaker Sizing with Safety Margin

I_breaker = (P / (V × cos θ)) × 1.25

Electrical Installations

Fuse/Breaker Current Rating

I_rating = P / V

Electrical Installations

Wire Resistance from Resistivity

R = ρ·L / A

Electrical Installations

Percentage Voltage Drop

%VD = (V_d / V_rated) × 100

Electrical Installations

Cable Voltage Drop (Single Phase)

V_d = (2 × L × I × R) / 1000

Power Systems

Short-Circuit Current

I_sc = V / Z_sc

Power Systems

Fault Level (MVA)

MVA_fault = kV² / Z

Power Systems

Power Factor Correction Capacitor Sizing

Q_C = P(tan θ₁ − tan θ₂)

Power Systems

Transformer kVA Rating

kVA = (V × I) / 1000

Power Systems

Star-Delta Line-Phase Relationship

Star: V_L=√3·V_ph, I_L=I_ph | Delta: V_L=V_ph, I_L=√3·I_ph

Power Systems

Power in kW (Three Phase)

P(kW) = (√3 × V_L × I_L × cos θ) / 1000

Power Systems

Power in kW (Single Phase)

P(kW) = (V × I × cos θ) / 1000

Energy & Billing

Utilization Factor

UF = Maximum Demand / Rated Capacity

Energy & Billing

Plant Capacity Factor

PCF = Average Load / Plant Capacity

Energy & Billing

Diversity Factor

DivF = ΣIndividual Max Demands / System Max Demand

Energy & Billing

Demand Factor

DF = Maximum Demand / Total Connected Load

Energy & Billing

Load Factor

LF = Average Load / Peak Load

Energy & Billing

Annual Energy Cost

Annual Cost = P(kW) × hours/day × 365 × rate

Energy & Billing

kWh to Joules Conversion

1 kWh = 3.6 × 10⁶ J

Energy & Billing

Cost of Running an Appliance

Cost = (Watts/1000) × hours × rate

Energy & Billing

kW to kVA Conversion

kVA = kW / cos θ

Energy & Billing

kVA to kW Conversion

kW = kVA × cos θ

Energy & Billing

Electricity Bill Cost

Cost = Energy(kWh) × Rate

Energy & Billing

Electrical Energy Consumption (kWh)

E(kWh) = P(kW) × t(hours)

Instrumentation & Measurement

Voltmeter Loading Error

V_measured = V_true · (R_m/(R_m+R_s))

Instrumentation & Measurement

Full-Scale Accuracy

Accuracy = 1 − (|error| / FSD)

Instrumentation & Measurement

Percentage Measurement Error

%Error = |(measured − true)/true| × 100

Instrumentation & Measurement

Sensor Sensitivity

S = Δoutput / Δinput

Instrumentation & Measurement

Common Mode Rejection Ratio

CMRR = A_d / A_cm

Instrumentation & Measurement

Op-Amp Slew Rate

SR = ΔV_out / Δt

Instrumentation & Measurement

Non-Inverting Op-Amp Gain

V_out = (1 + R_f/R_in)·V_in

Instrumentation & Measurement

Inverting Op-Amp Gain

V_out = −(R_f/R_in)·V_in

Instrumentation & Measurement

Instrumentation Amplifier Gain

G = (1 + 2R₂/R_g)(R₄/R₃)

Instrumentation & Measurement

RTD Resistance-Temperature Relation

R_T = R₀(1 + αΔT)

Instrumentation & Measurement

Thermocouple Seebeck Voltage

V = S·ΔT

Instrumentation & Measurement

Strain Gauge Factor

GF = (ΔR/R) / ε

Control Systems

Gain Margin

GM = 1 / |G(jω_pc)|

Control Systems

Steady-State Error

e_ss = lim_{s→0} s·E(s)

Control Systems

Natural Frequency (Electrical Analog)

ω_n = 1 / √(LC)

Control Systems

Damping Ratio (Electrical Analog)

ζ = R/2 · √(C/L)

Control Systems

PID Controller Output

u(t) = K_p·e + K_i∫e dt + K_d·(de/dt)

Control Systems

Transfer Function

H(s) = Y(s) / X(s)

Transmission Lines

Return Loss

RL = −20·log₁₀|Γ|

Transmission Lines

Phase Velocity

v_p = 1 / √(LC)

Transmission Lines

Propagation Constant

γ = √(Z·Y)

Transmission Lines

Standing Wave Ratio

SWR = (1 + |Γ|) / (1 − |Γ|)

Transmission Lines

Reflection Coefficient

Γ = (Z_L − Z₀) / (Z_L + Z₀)

Transmission Lines

Characteristic Impedance

Z₀ = √(L/C)

Electric Machines

Armature Current of a DC Motor

I_a = (V − E_b) / R_a

Electric Machines

Generator EMF Equation

E = 4.44·f·N·Φ

Electric Machines

Motor Efficiency

η = P_out / P_in

Electric Machines

Torque of a DC Motor

T = k·Φ·I_a

Electric Machines

Back EMF of a DC Motor

E_b = V − I_a·R_a

Electric Machines

Slip of an Induction Motor

s = (N_s − N_r) / N_s

Electric Machines

Synchronous Speed

N_s = 120·f / P

Signal Processing

Z-Transform

X(z) = Σ x[n]·z^(−n)

Signal Processing

Bit Rate

R = 1 / T_b

Signal Processing

Signal-to-Noise Ratio

SNR = P_signal / P_noise

Signal Processing

Decibel (Voltage/Amplitude Ratio)

dB = 20·log₁₀(V₂/V₁)

Signal Processing

Decibel (Power Ratio)

dB = 10·log₁₀(P₂/P₁)

Signal Processing

Convolution

y(t) = x(t) * h(t)

Signal Processing

Laplace Transform

X(s) = ∫x(t)·e^(−st) dt

Signal Processing

Fourier Transform

X(f) = ∫x(t)·e^(−j2πft) dt

Digital Electronics

Clock Frequency-Period Relation

f = 1 / T

Digital Electronics

Propagation Delay

t_pd = (t_pHL + t_pLH) / 2

Digital Electronics

Nyquist Sampling Rate

f_s ≥ 2·f_max

Digital Electronics

Shannon's Channel Capacity

C = B·log₂(1 + S/N)

Digital Electronics

Binary to Decimal Conversion

D = Σ b_i · 2^i

Digital Electronics

De Morgan's Theorem

(A·B)' = A' + B'

Digital Electronics

Boolean OR Operation

Y = A + B

Digital Electronics

Boolean AND Operation

Y = A · B

Semiconductor Devices

Zener Diode Voltage Regulation

V_out ≈ V_Z

Semiconductor Devices

CMOS Dynamic Power Dissipation

P = C·V²·f

Semiconductor Devices

MOSFET Transconductance

g_m = 2I_D / (V_GS − V_T)

Semiconductor Devices

Diode Small-Signal Resistance

r_d = V_T / I_D

Semiconductor Devices

BJT Collector Current (Early Effect)

I_C = I_S·e^(V_BE/V_T)·(1 + V_CE/V_A)

Semiconductor Devices

BJT Emitter Current

I_E = I_C + I_B

Semiconductor Devices

MOSFET Saturation Current

I_D = ½k(V_GS − V_T)²

AC Circuits

Skin Depth

δ = √(2ρ / (ωμ))

AC Circuits

Admittance

Y = 1 / Z

AC Circuits

RLC Series Impedance

Z = R + j(X_L − X_C)

AC Circuits

Phasor Voltage Representation

V = V_m∠θ

AC Circuits

Bandwidth of a Resonant Circuit

BW = f₀ / Q

AC Circuits

Quality Factor (Series RLC)

Q = ω₀L / R

AC Circuits

Angular Frequency

ω = 2π·f

AC Circuits

Impedance of a Capacitor

Z_C = 1 / (jωC)

AC Circuits

Impedance of an Inductor

Z_L = jωL

AC Circuits

Impedance of a Resistor

Z_R = R

Magnetics

Magnetic Force on a Current-Carrying Wire

F = B·I·L·sin θ

Magnetics

Magnetic Field of a Solenoid

B = μ₀·n·I

Magnetics

Lorentz Force Law

F = q(E + v × B)

Magnetics

Biot–Savart Law

dB = (μ₀/4π)·(I·dl × r̂)/r²

Magnetics

Ampere's Law

∮B·dl = μ₀·I_enc

Electromagnetics

Poynting Vector

S = E × H

Electromagnetics

Electric Dipole Moment

p = q·d

Electromagnetics

Dielectric Constant Relation

C = ε_r·C₀

Electromagnetics

Electric Potential (Point Charge)

V = k·Q / r

Electromagnetics

Electric Potential Energy

U = q·V

Electromagnetics

Gauss's Law

∮E·dA = Q_enc / ε₀

Power Systems

Base Impedance (Per-Unit System)

Z_base = V_base² / S_base

Power Systems

Line Losses

P_loss = I²·R

Power Systems

Voltage Regulation

VR = (V_NL − V_FL)/V_FL × 100%

Power Systems

Electrical Efficiency

η = (P_out / P_in) × 100%

Power Systems

Transformer Power Conservation

V₁·I₁ = V₂·I₂

Power Systems

Transformer Turns Ratio

V₁/V₂ = N₁/N₂

Power Systems

Power Triangle Relation

S² = P² + Q²

Power Systems

Complex Power

S = P + jQ

Power Systems

Three-Phase Power (Line Values)

P = √3·V_L·I_L·cos θ

Circuit Analysis

Wheatstone Bridge Balance Condition

R₁/R₂ = R₃/R₄

Circuit Analysis

Capacitor Charge Relation

Q = C·V

Circuit Analysis

Energy Stored in an Inductor

E = ½L·I²

Circuit Analysis

Energy Stored in a Capacitor

E = ½C·V²

Circuit Analysis

Inductor Current Growth

I(t) = (V/R)(1 − e^(−tR/L))

Circuit Analysis

Capacitor Discharging Voltage

V(t) = V₀·e^(−t/RC)

Circuit Analysis

Capacitor Charging Voltage

V(t) = V₀(1 − e^(−t/RC))

Circuit Analysis

RL Time Constant

τ = L / R

Circuit Analysis

RC Time Constant

τ = R·C

Circuit Analysis

Current Divider Rule

I_x = I_in · (R_T / R_x)

Circuit Analysis

Delta-to-Wye Transformation

R_a = (R_ab·R_ca) / (R_ab+R_bc+R_ca)

Circuit Analysis

Millman's Theorem

V = (ΣI_k) / (ΣG_k)

Circuit Analysis

Maximum Power Transfer Theorem

P_max occurs when R_L = R_TH

Circuit Analysis

Thevenin's Theorem Equivalent Resistance

R_TH = V_OC / I_SC

Circuit Analysis

Norton's Theorem Equivalent Current

I_N = I_SC

Electromagnetics

Capacitance (Parallel Plate)

C = εA / d

Electromagnetics

Coulomb's Law

F = k·q₁q₂ / r²

Power Systems

Apparent Power (AC)

S = V · I*

Power Systems

Electrical Power (DC)

P = V · I

Circuit Analysis

Voltage Divider Rule

V_x = V_in · (R_x / R_T)

Circuit Analysis

Parallel Resistance

1/R_T = 1/R₁ + 1/R₂

Circuit Analysis

Series Resistance

R_T = R₁ + R₂ + ... + Rₙ

Circuit Analysis

Kirchhoff's Current Law

ΣI_in = ΣI_out

Circuit Analysis

Kirchhoff's Voltage Law

ΣV = 0